Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9751	6^127458-17993	99182	Enzo Doria	03/2013
9752	27197^4428+4428^27197	99166	Hans Havermann	10/2017
9753	(46*10^99143-1)/9	99144	Robert Price	12/2014
9754	(64*10^99135+161)/9	99136	Robert Price	08/2022
9755	7*10^99133+69	99134	Robert Price	10/2017
9756	(21701^22861-1)/21700	99132	Serge Batalov	06/2022
9757	18^78968-3065	99127	Enzo Doria	03/2013
9758	25927^6654+6654^25927	99122	Hans Havermann	10/2017
9759	87915!4+16	99122	Robert Price	09/2019
9760	2^329259+189	99117	Lelio R Paula	12/2012
9761	8*10^99113+39	99114	Robert Price	01/2017
9762	6^127364+77	99109	Lelio R Paula	08/2016
9763	(82*10^99103+143)/9	99104	Robert Price	06/2021
9764	(11414^24421-1)/11413	99083	Serge Batalov	06/2022
9765	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
9766	(22089^22807-1)/22088	99074	Serge Batalov	06/2022
9767	(59*10^99069+391)/9	99070	Robert Price	03/2021
9768	(797*10^99061-41)/9	99063	Robert Price	04/2022
9769	2^329058-287681	99057	Harrison Mesh	06/2022
9770	6^127285+13	99047	Lelio R Paula	08/2016
9771	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
9772	2^329007+73283	99041	Enzo Doria	04/2016
9773	(145413^19321-1)/(145413^139-1)	99030	Ryan Propper	11/2023
9774	5*3^207543-8	99024	Lelio R Paula	08/2014
9775	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
9776	2^328885+149	99005	Lelio R Paula	12/2012
9777	23392^17075+17075^23392	99004	Hans Havermann	09/2017
9778	(7424^25579-1)/7423	99004	Serge Batalov	06/2022
9779	(2^328879-9)/119	99001	Lelio R Paula	10/2013
9780	5^141618+54	98987	Lelio R Paula	08/2016
9781	2^328824+24391	98986	Enzo Doria	10/2023
9782	8*10^98982+51	98983	Robert Price	05/2017
9783	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
9784	2^328794-2797601	98977	Enzo Doria	04/2016
9785	(88331^20011-1)/88330	98972	Serge Batalov	06/2022
9786	6^127176+5	98963	Lelio R Paula	11/2014
9787	2*10^98961-21	98962	Robert Price	09/2020
9788	24262^11989+11989^24262	98960	Hans Havermann	09/2017
9789	(60138^20707-1)/60137	98958	Serge Batalov	06/2022
9790	2^328700-109709	98949	Enzo Doria	04/2014
9791	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
9792	(1014^32917-1)/1013	98947	Serge Batalov	06/2022
9793	87771!4-128	98944	Robert Price	11/2019
9794	(4576^27031-1)/4575	98943	Serge Batalov	06/2022
9795	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
9796	(1933^30103-1)/1932	98923	Serge Batalov	06/2022
9797	46711!2-2^46711	98916	Robert Price	09/2015
9798	9*7^117037+4	98909	Lelio R Paula	11/2014
9799	127^47012+126	98905	Norbert Schneider	01/2019
9800	(93826^19891-1)/93825	98900	Serge Batalov	06/2022
9801	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
9802	(10^98890+149)/3	98890	Serge Batalov	12/2014
9803	22775^21978+21978^22775	98889	Hans Havermann	08/2017
9804	2^328497-216933	98888	Enzo Doria	05/2014
9805	2^328487+32769	98885	Lelio R Paula	08/2016
9806	3^207250-112358	98884	Enzo Doria	06/2014
9807	13^88754-90	98867	Lelio R Paula	08/2016
9809	2^328406+709	98861	Lelio R Paula	02/2013
9808	2*10^98860-21	98861	Robert Price	09/2020
9810	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
9811	7^116976+76	98857	Lelio R Paula	08/2016
9812	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
9813	(25411^22441-1)/25410	98849	Serge Batalov	06/2022
9814	(18668^23143-1)/18667	98842	Serge Batalov	06/2022
9816	2^328335+1155	98839	Lelio R Paula	08/2016
9815	2^328333-349003	98839	Harrison Mesh	06/2022
9818	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
9817	287^40210+40210^287	98832	Norbert Schneider	11/2014
9819	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
9820	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
9821	(28623^22171-1)/28622	98806	Serge Batalov	06/2022
9822	24746^9825+9825^24746	98795	Hans Havermann	07/2020
9823	26620^5143+5143^26620	98793	Hans Havermann	07/2020
9824	65^54491+48	98788	Lelio R Paula	04/2016
9825	3^207042+98	98785	Lelio R Paula	08/2016
9826	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
9827	10^98754+73383	98755	Patrick De Geest	02/2021
9830	3^206977-112756	98754	Enzo Doria	07/2014
9829	10^98754-40000000001	98754	Robert Price	09/2020
9828	10^98754-169343	98754	Patrick De Geest	02/2021
9831	7^116846-50	98747	Lelio R Paula	08/2016
9832	(19152^23059-1)/19151	98740	Serge Batalov	06/2022
9833	23267^17512+17512^23267	98730	Hans Havermann	04/2020
9834	2^327967-28635	98728	Lelio R Paula	08/2016
9835	707^34642+34642^707	98710	Norbert Schneider	12/2017
9836	(10771^24481-1)/10770	98710	Serge Batalov	06/2022
9837	6^126850-47	98709	Lelio R Paula	08/2016
9838	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
9839	(22*10^98697+47)/3	98698	Robert Price	06/2021
9840	(139706^19321-1)/(139706^139-1)	98696	Ryan Propper	11/2023
9841	8*6^126830-7	98694	Lelio R Paula	11/2014
9842	11^94770-270	98693	Enzo Doria	08/2012
9843	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
9844	2^327832+43	98688	Lelio R Paula	12/2012
9845	2^327795+761	98677	Lelio R Paula	02/2013
9846	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
9847	10^98669+147411	98670	Patrick De Geest	11/2016
9849	10^98669-9^(98669-1)	98669	Robert Price	05/2016
9848	10^98669-105249	98669	Patrick De Geest	11/2016
9850	(7911^25309-1)/7910	98657	Serge Batalov	06/2022
9851	2^327671-109801	98639	Enzo Doria	04/2014
9852	24398^11037+11037^24398	98638	Hans Havermann	10/2019
9853	5^141090-14	98618	Lelio R Paula	08/2016
9854	20^75799+47	98617	Lelio R Paula	08/2016
9855	(5452^26393-1)/5451	98616	Serge Batalov	06/2022
9856	28101^3226+3226^28101	98597	Hans Havermann	07/2020
9857	2^327515-1017	98592	Lelio R Paula	08/2016
9858	6^126692+97681	98586	Mike Oakes	04/2011
9859	2^327467-741	98578	Lelio R Paula	08/2016
9860	(2947^28411-1)/2946	98566	Serge Batalov	06/2022
9861	22713^21800+21800^22713	98540	Hans Havermann	05/2020
9862	(2^327329+9)/19	98535	Lelio R Paula	10/2013
9863	7^116577-66	98519	Lelio R Paula	08/2016
9865	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
9864	23220^17479+17479^23220	98512	Hans Havermann	03/2020
9866	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
9867	(28514^22111-1)/28513	98502	Serge Batalov	06/2022
9868	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
9869	2^327162-66945	98486	Lelio R Paula	08/2016
9870	30139^1852+1852^30139	98484	Hans Havermann	02/2020
9871	23182^17703+17703^23182	98479	Hans Havermann	01/2020
9872	4*10^98472-3	98473	Erik Branger	11/2013
9873	26167^5794+5794^26167	98466	Hans Havermann	01/2020
9874	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
9875	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
9876	(2009^29803-1)/2008	98436	Serge Batalov	06/2022
9877	13^88363+94	98432	Lelio R Paula	08/2016
9878	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
9879	6^126481+41	98422	Lelio R Paula	08/2016
9880	78*10^98413-7	98415	Robert Price	05/2017
9881	22634^22263+22263^22634	98404	Hans Havermann	07/2020
9882	(47*10^98386+241)/9	98387	Robert Price	06/2022
9883	7^116416+46	98383	Lelio R Paula	08/2016
9884	7^116407-24	98376	Lelio R Paula	07/2016
9885	439^37228+37228^439	98374	Norbert Schneider	08/2018
9886	2^326782-1860671	98372	Enzo Doria	03/2016
9887	17^79948+58	98372	Lelio R Paula	08/2016
9888	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
9889	3^206143-98	98356	Lelio R Paula	08/2016
9890	8*5^140705+7	98350	Lelio R Paula	11/2014
9891	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
9892	(638^35053-1)/637	98315	Serge Batalov	06/2022
9893	2^326585+11	98312	Lelio R Paula	12/2012
9894	2^326582-459161	98311	Enzo Doria	05/2015
9895	(1266^31687-1)/1265	98304	Serge Batalov	06/2022
9897	(2^326548+9)/5	98301	Lelio R Paula	10/2013
9896	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
9898	2^326538+71659	98298	Enzo Doria	04/2016
9899	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
9900	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
9901	15^83575-58	98292	Lelio R Paula	08/2016
9902	10^98288+3	98289	Robert Price	03/2011
9903	10^98288-117017	98288	Patrick De Geest	11/2011
9904	(44*10^98284-719)/9	98285	Robert Price	12/2017
9905	(5985^26021-1)/5984	98280	Serge Batalov	06/2022
9906	23466^15419+15419^23466	98277	Hans Havermann	02/2020
9907	2^326421-2797573	98263	Enzo Doria	04/2016
9908	2^326401+16095	98257	Lelio R Paula	07/2016
9909	(6494^25771-1)/6493	98249	Serge Batalov	06/2022
9910	7^116240-116240^7	98235	Norbert Schneider	05/2017
9911	17^79826-78	98222	Lelio R Paula	08/2016
9912	2^326268-809	98217	Yves Minet	04/2011
9913	22659^21590+21590^22659	98210	Hans Havermann	10/2019
9914	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
9915	(418*10^98199+23)/9	98201	Robert Price	08/2017
9916	12*10^98198-7	98200	Robert Price	11/2017
9917	15^83496-76	98199	Lelio R Paula	08/2016
9918	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
9919	9*5^140471-4	98186	Lelio R Paula	11/2014
9920	(35103^21601-1)/35102	98180	Serge Batalov	06/2022
9922	22774^20455+20455^22774	98175	Hans Havermann	07/2020
9921	(4516^26863-1)/4515	98175	Serge Batalov	06/2022
9923	2^326069-2383	98157	Yves Minet	10/2013
9924	(9661^24631-1)/9660	98152	Serge Batalov	06/2022
9925	(4175^27109-1)/4174	98149	Serge Batalov	06/2022
9926	(57801^20611-1)/57800	98144	Serge Batalov	06/2022
9927	2^325973+1185	98128	Lelio R Paula	07/2016
9928	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
9929	2^325945-1847269	98120	Enzo Doria	07/2015
9930	8*10^98111-67	98112	Robert Price	10/2017
9931	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
9932	(215^42061-1)/214	98103	Serge Batalov	06/2022
9933	(6775^25609-1)/6774	98102	Serge Batalov	06/2022
9934	(6718^25633-1)/6717	98100	Serge Batalov	06/2022
9935	2^325866+15	98096	Lelio R Paula	12/2012
9936	22591^21952+21952^22591	98079	Hans Havermann	02/2020
9937	2^325765+1974305	98066	Enzo Doria	06/2016
9938	2^325733-58695	98056	Lelio R Paula	07/2016
9939	(7*10^98055-529)/9	98055	Robert Price	08/2021
9940	2^325717-3645	98051	Lelio R Paula	07/2016
9941	(2^325704+718)/2	98047	Stefano Morozzi	09/2020
9942	(15679^23371-1)/15678	98045	Serge Batalov	06/2022
9943	(23342^22441-1)/23341	98022	Serge Batalov	06/2022
9944	23968^12293+12293^23968	98021	Hans Havermann	11/2019
9946	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
9945	(128678^19321-1)/(128678^139-1)	98011	Ryan Propper	11/2023
9947	(7*10^98007-13)/3	98008	Robert Price	06/2016
9948	(2^325544+1110)/2	97999	Stefano Morozzi	09/2020
9949	2^325512-459959	97989	Enzo Doria	05/2015
9950	(2^325492+682)/2	97983	Stefano Morozzi	09/2020
9951	(3^205354-8)/17	97978	Lelio R Paula	09/2013
9952	2^325433+76817	97966	Enzo Doria	05/2016
9953	5*10^97963+81	97964	Robert Price	08/2017
9954	(9996^24649-1)/(9996^157-1)	97964	Ryan Propper	11/2023
9955	(13208^23773-1)/13207	97961	Serge Batalov	06/2022
9956	2^325390-109061	97953	Enzo Doria	04/2014
9957	(55*10^97940+323)/9	97941	Robert Price	10/2021
9958	13^87921+24	97940	Lelio R Paula	08/2016
9959	10^97930+188277	97931	Patrick De Geest	09/2022
9961	10^97930-7000001	97930	Robert Price	06/2021
9960	10^97930-66951	97930	Patrick De Geest	09/2022
9962	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
9963	(17968^23017-1)/17967	97922	Serge Batalov	06/2022
9964	(3337^27793-1)/3336	97922	Serge Batalov	06/2022
9966	22600^21499+21499^22600	97913	Hans Havermann	05/2020
9965	(18703^22921-1)/18702	97913	Serge Batalov	06/2022
9967	2^325215+12909	97900	Lelio R Paula	07/2016
9968	22619^21286+21286^22619	97898	Hans Havermann	04/2020
9969	(126852^19321-1)/(126852^139-1)	97892	Ryan Propper	11/2023
9970	(85*10^97876-49)/9	97877	Robert Price	12/2020
9971	7*10^97874-69	97875	Robert Price	01/2017
9972	5*10^97869-63	97870	Robert Price	04/2021
9973	(643*32^65022-23)/31	97870	Eric Chen	04/2023
9975	(17^79537+5^79537)/22	97865	Robert Price	06/2013
9974	15^83212+22	97865	Lelio R Paula	08/2016
9976	2^325087-109057	97861	Enzo Doria	04/2014
9977	2^325074+1870657	97858	Enzo Doria	05/2016
9979	2^325066-2111	97855	Yves Minet	08/2013
9978	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
9980	(8694^24841-1)/8693	97851	Serge Batalov	06/2022
9981	(21159^22621-1)/21158	97843	Serge Batalov	06/2022
9982	26660^4677+4677^26660	97842	Hans Havermann	12/2019
9983	18^77944-89	97841	Lelio R Paula	07/2016
9984	119^47136+118	97833	Norbert Schneider	09/2018
9985	6^125720-17663	97830	Enzo Doria	02/2013
9986	(73640^20101-1)/73639	97829	Serge Batalov	06/2022
9987	2^324972-2069	97827	Yves Minet	05/2013
9988	2^324958-4691	97823	Yves Minet	05/2019
9989	(8087^25033-1)/8086	97820	Serge Batalov	06/2022
9990	2^324944-2788319	97818	Enzo Doria	03/2016
9992	22845^19112+19112^22845	97807	Hans Havermann	10/2019
9991	(317^39107-1)/316	97807	Anonymous	04/2024
9993	(2^324898+1270)/2	97804	Stefano Morozzi	09/2020
9995	4*10^97799-9	97800	Erik Branger	11/2013
9994	2^324882+577294575	97800	Lelio R Paula	09/2016
9996	2^324863-1867921	97794	Enzo Doria	04/2016
9997	6^125662-18473	97785	Enzo Doria	03/2013
9998	12^90604+11	97779	Lelio R Paula	07/2016
9999	(29*10^97751+49)/3	97752	Robert Price	09/2021
10000	(37108^21391-1)/37107	97741	Serge Batalov	06/2022

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Probable Primes Top 10000

(295532 PRPs in the top)